plug in your pad and make sure its calibrated in windows controler setup (found in control panel devices and printers) i think)) then open psx controler options and select the controler your using. it may ask you to define the bottons and sticks. just click on each with the mouse and press the respective buttons or stick on the pad. 1s done you should have full control...
From what I remeber with PCSX you have to map each of the controllers buttons to the corrisponding buttons on the controller emulator tab, but even with the PS2 to PC-USB converter you probably wouldn't get full controller emulation because the D-Pad and control buttons (X,O,□,Δ) are pressure sensitive and I'm assuming the control buttons will only be supported as simple digital buttons.
i have a logitech dual action which is absolutely identical to the ps2 handset. right town to the pressure sensitive buttons. the only difference is its usb2 only. at around £14.99(how much mine cost) its 1 of the best controlers i have bought for the money... mine is 5 years old and still fully working and im not exactly gentle with it...
so the build quality is up to logitechs higher standard.